Subgroups — C₂²×#11719511 #16769839

Order 3328.

14462 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6129	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11719511	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#88190	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88189	C₂	1	2	yes	maximal, complemented
5	C₂²×#88178	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88193	C₂	1	2	yes	maximal, complemented
7	C₂²×#88192	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#88207	C₂	1	2	yes	maximal, complemented
9	C₂²×D₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₂²⋊Dic₁₃	C₂	1	2	yes	maximal, complemented
12	C₂⁴×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁶×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	—	2	16	no	—
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	24	yes	complemented
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
21	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
22	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
23	C₂⁴×Dic₁₃	C₂²	1	2	yes	complemented
24	C₂⁴×Dic₁₃	C₂²	1	2	yes	complemented
25	C₂²×#6129	—	2	16	no	—
26	C₂²×#6129	C₂²	1	24	yes	complemented
27	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×#88207	C₂²	1	48	yes	complemented
30	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
32	C₂²×C₂²⋊Dic₁₃	C₂²	1	48	yes	complemented
33	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
36	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
37	#11719511	C₂²	1	256	yes	direct product factor
38	C₂×#88193	C₂²	1	48	yes	complemented
39	C₂×#88192	C₂²	1	24	yes	complemented
40	C₂×#88190	C₂²	1	24	yes	complemented
41	C₂×#88189	C₂²	1	48	yes	complemented
42	C₂×D₄×Dic₁₃	C₂²	1	24	yes	complemented
43	C₂×C₄×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
44	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×#88178	C₂²	1	24	yes	complemented
47	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
48	C₂²×#6101	C₂²	1	2	yes	complemented
49	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
50	C₂⁵×C₁₃	—	2	16	no	—
51	C₂⁵×C₁₃	—	2	16	no	—
52	C₂⁵×C₁₃	—	4	8	no	—
53	C₂⁵×C₁₃	C₂³	1	2	yes	—
54	C₂⁵×C₁₃	C₂³	1	24	yes	—
55	C₂⁵×C₁₃	C₂³	1	2	yes	—
56	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
57	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	16	no	—
59	C₂²×D₄×C₁₃	—	2	192	no	—
60	C₂²×D₄×C₁₃	—	2	8	no	—
61	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
62	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	64	yes	complemented
66	C₂³×C₄×C₁₃	—	2	8	no	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₂²⋊D₁₃	—	2	16	no	—
71	C₂²×C₂²⋊D₁₃	—	2	8	no	—
72	C₂²×C₂²⋊D₁₃	—	4	8	no	—
73	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
74	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	complemented
75	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	complemented
76	C₂³×Dic₁₃	—	2	16	no	—
77	C₂³×Dic₁₃	—	4	8	no	—
78	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
79	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
80	C₂³×Dic₁₃	C₂³	1	2	yes	—
81	C₂³×Dic₁₃	C₂³	1	2	yes	—
82	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
83	C₂³×Dic₁₃	C₂³	1	24	yes	complemented
84	C₂³×Dic₁₃	C₂³	1	24	yes	complemented
85	C₂×#6129	—	2	192	no	—
86	C₂×#6129	C₂³	1	64	yes	complemented
87	C₂²×C₄×D₁₃	—	2	8	no	—
88	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
89	C₂²×Dic₂₆	—	2	8	no	—
90	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
91	#88207	C₂³	1	128	yes	complemented
92	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
93	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
94	C₂×C₂²⋊Dic₁₃	C₂³	1	128	yes	complemented
95	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	complemented
96	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	complemented
97	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	complemented
98	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	complemented
99	#88193	C₂³	1	128	yes	complemented
100	#88192	C₂³	1	64	yes	complemented
101	#88190	C₂³	1	64	yes	complemented
102	#88189	C₂³	1	128	yes	complemented
103	D₄×Dic₁₃	C₂³	1	64	yes	complemented
104	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
105	C₂×#6103	C₂³	1	12	yes	complemented
106	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
107	#88178	C₂³	1	64	yes	complemented
108	C₂×#6101	C₂³	1	24	yes	complemented
109	C₂×#6101	C₂³	1	12	yes	complemented
110	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
111	C₂²×#546	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	—	2	8	no	—
114	C₂⁴×C₁₃	—	2	8	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	2	96	no	—
117	C₂⁴×C₁₃	—	2	8	no	—
118	C₂⁴×C₁₃	—	2	8	no	—
119	C₂⁴×C₁₃	—	2	96	no	—
120	C₂⁴×C₁₃	—	2	8	no	—
121	C₂⁴×C₁₃	—	4	48	no	—
122	C₂⁴×C₁₃	—	4	128	no	—
123	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
124	C₂⁴×C₁₃	#41	1	8	yes	complemented
125	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	32	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
128	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
129	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂³×D₁₃	—	2	4	no	—
131	C₂³×D₁₃	—	2	4	no	—
132	C₂³×D₁₃	—	2	4	no	—
133	C₂³×D₁₃	C₂⁴	1	6	yes	—
134	C₂×D₄×C₁₃	—	2	96	no	—
135	C₂×D₄×C₁₃	—	2	256	no	—
136	C₂×D₄×C₁₃	—	2	48	no	—
137	C₂×D₄×C₁₃	C₂×D₄	1	96	yes	complemented
138	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
139	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
140	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	48	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
147	C₂×C₂²⋊D₁₃	—	2	96	no	—
148	C₂×C₂²⋊D₁₃	—	2	48	no	—
149	C₂×C₂²⋊D₁₃	—	4	48	no	—
150	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
151	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
152	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
153	C₂²×Dic₁₃	—	2	8	no	—
154	C₂²×Dic₁₃	—	2	4	no	—
155	C₂²×Dic₁₃	—	2	96	no	—
156	C₂²×Dic₁₃	—	2	4	no	—
157	C₂²×Dic₁₃	—	2	4	no	—
158	C₂²×Dic₁₃	—	2	8	no	—
159	C₂²×Dic₁₃	—	4	48	no	—
160	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
161	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
162	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
163	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
164	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
165	C₂²×Dic₁₃	C₂⁴	1	32	yes	complemented
166	C₂²×Dic₁₃	C₂⁴	1	32	yes	complemented
167	#6129	—	2	256	no	—
168	C₂×C₄×D₁₃	—	2	48	no	—
169	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
170	C₂×Dic₂₆	—	2	48	no	—
171	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
172	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
173	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
174	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
175	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
176	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
177	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
178	#6103	C₂⁴	1	16	yes	complemented
179	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
180	#6101	C₂⁴	1	32	yes	complemented
181	#6101	C₂⁴	1	16	yes	complemented
182	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
183	C₂³×#41	—	13	1	no	—
184	C₂⁴×D₄	D₁₃	1	1	yes	characteristic, complemented
185	C₂×#546	—	13	48	no	—
186	C₂²×#124	—	13	1	no	—
187	C₂²×#123	—	13	2	no	—
188	C₂²×C₂²⋊Q₈	—	13	1	no	—
189	C₂²×#121	—	13	1	no	—
190	C₂²×#121	—	13	2	no	—
191	C₂²×#120	—	13	2	no	—
192	C₂²×C₄×D₄	—	13	1	no	—
193	C₂²×C₄×D₄	—	13	1	no	—
194	C₂³×C₂²⋊C₄	—	13	2	no	—
195	C₂³×C₁₃	—	2	32	no	—
196	C₂³×C₁₃	—	2	64	no	—
197	C₂³×C₁₃	—	2	12	no	—
198	C₂³×C₁₃	—	2	24	no	—
199	C₂³×C₁₃	—	2	24	no	—
200	C₂³×C₁₃	—	2	12	no	—
201	C₂³×C₁₃	—	2	64	no	—
202	C₂³×C₁₃	—	2	24	no	—
203	C₂³×C₁₃	—	2	24	no	—
204	C₂³×C₁₃	—	2	64	no	—
205	C₂³×C₁₃	—	2	24	no	—
206	C₂³×C₁₃	—	4	32	no	—
207	C₂³×C₁₃	—	4	384	no	—
208	C₂³×C₁₃	—	4	32	no	—
209	C₂³×C₁₃	C₂²×D₄	1	48	yes	—
210	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
211	C₂³×C₁₃	C₂×#41	1	4	yes	—
212	C₂³×C₁₃	C₂×#41	1	24	yes	complemented
213	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
214	C₂³×C₁₃	C₂⁵	1	8	yes	—
215	C₂³×C₁₃	C₂⁵	1	8	yes	—
216	C₂³×C₁₃	C₂⁵	1	4	yes	—
217	C₂³×C₁₃	C₂⁵	1	3	yes	—
218	C₂²×D₁₃	—	2	12	no	—
219	C₂²×D₁₃	—	2	12	no	—
220	C₂²×D₁₃	—	2	12	no	—
221	C₂²×D₁₃	—	4	16	no	—
222	C₂²×D₁₃	C₂⁵	1	4	yes	—
223	D₄×C₁₃	—	2	64	no	—
224	D₄×C₁₃	—	2	32	no	—
225	D₄×C₁₃	C₂²×D₄	1	64	yes	complemented
226	C₂×C₄×C₁₃	—	2	12	no	—
227	C₂×C₄×C₁₃	—	2	32	no	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
229	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
231	C₂²⋊D₁₃	—	2	64	no	—
232	C₂²⋊D₁₃	—	2	32	no	—
233	C₂²⋊D₁₃	—	4	32	no	—
234	C₂×Dic₁₃	—	2	24	no	—
235	C₂×Dic₁₃	—	2	12	no	—
236	C₂×Dic₁₃	—	2	64	no	—
237	C₂×Dic₁₃	—	2	12	no	—
238	C₂×Dic₁₃	—	2	12	no	—
239	C₂×Dic₁₃	—	2	24	no	—
240	C₂×Dic₁₃	—	4	32	no	—
241	C₂×Dic₁₃	C₂⁵	1	4	yes	—
242	C₂×Dic₁₃	C₂⁵	1	4	yes	—
243	C₂×Dic₁₃	C₂⁵	1	8	yes	—
244	C₂×Dic₁₃	C₂⁵	1	8	yes	—
245	C₂×Dic₁₃	C₂⁵	1	4	yes	—
246	C₄×D₁₃	—	2	32	no	—
247	Dic₂₆	—	2	32	no	—
248	C₂⁶	C₂×D₁₃	1	2	yes	—
249	C₂²×#41	—	13	24	no	—
250	C₂²×#41	—	26	16	no	—
251	C₂³×Q₈	—	13	1	no	—
252	C₂³×D₄	—	2	16	no	—
253	C₂³×D₄	—	13	2	no	—
254	C₂³×D₄	—	13	1	no	—
255	C₂³×D₄	—	13	2	no	—
256	C₂³×D₄	C₂×D₁₃	1	2	yes	—
257	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
258	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
259	C₂³×D₄	C₂×D₁₃	1	24	yes	complemented
260	C₂⁴×C₄	—	13	2	no	—
261	C₂⁴×C₄	—	13	2	no	—
262	C₂⁴×C₄	—	13	1	no	—
263	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
264	#546	—	13	256	no	—
265	C₂×#124	—	13	24	no	—
266	C₂×#123	—	13	48	no	—
267	C₂×C₂²⋊Q₈	—	13	24	no	—
268	C₂×#121	—	13	24	no	—
269	C₂×#121	—	13	48	no	—
270	C₂×#120	—	13	48	no	—
271	C₂×C₄×D₄	—	13	24	no	—
272	C₂×C₄×D₄	—	13	24	no	—
273	C₂²×C₄⋊C₄	—	13	1	no	—
274	C₂²×C₄⋊C₄	—	13	2	no	—
275	C₂²×C₄⋊C₄	—	13	1	no	—
276	C₂²×C₂²⋊C₄	—	13	1	no	—
277	C₂²×C₂²⋊C₄	—	13	2	no	—
278	C₂²×C₂²⋊C₄	—	13	2	no	—
279	C₂²×C₂²⋊C₄	—	13	2	no	—
280	C₂²×C₂²⋊C₄	—	13	48	no	—
281	C₂²×C₂²⋊C₄	—	13	2	no	—
282	C₂²×C₂²⋊C₄	—	13	2	no	—
283	C₂²×C₂²⋊C₄	—	13	1	no	—
284	C₂²×C₄²	—	13	1	no	—
285	C₂²×C₁₃	—	2	4	no	—
286	C₂²×C₁₃	—	2	8	no	—
287	C₂²×C₁₃	—	2	8	no	—
288	C₂²×C₁₃	—	2	4	no	—
289	C₂²×C₁₃	—	2	48	no	—
290	C₂²×C₁₃	—	2	96	no	—
291	C₂²×C₁₃	—	2	8	no	—
292	C₂²×C₁₃	—	2	8	no	—
293	C₂²×C₁₃	—	2	8	no	—
294	C₂²×C₁₃	—	4	128	no	—
295	C₂²×C₁₃	—	4	48	no	—
296	C₂²×C₁₃	#546	1	16	yes	complemented
297	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
298	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
299	C₂²×C₁₃	C₂²×#41	1	6	yes	—
300	C₂²×C₁₃	C₂²×#41	1	8	yes	complemented
301	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
302	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
303	C₂×D₁₃	—	2	4	no	—
304	C₂×D₁₃	—	2	4	no	—
305	C₂×D₁₃	—	2	4	no	—
306	C₂×D₁₃	—	4	24	no	—
307	C₄×C₁₃	—	2	4	no	—
308	C₄×C₁₃	C₂³×D₄	1	8	yes	—
309	Dic₁₃	—	2	8	no	—
310	Dic₁₃	—	2	4	no	—
311	Dic₁₃	—	2	4	no	—
312	Dic₁₃	—	2	4	no	—
313	Dic₁₃	—	2	8	no	—
314	C₂⁵	—	2	16	no	—
315	C₂⁵	—	2	16	no	—
316	C₂⁵	—	4	8	no	—
317	C₂⁵	—	13	1	no	—
318	C₂⁵	C₂²×D₁₃	1	2	yes	—
319	C₂⁵	C₂²×D₁₃	1	24	yes	—
320	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
321	C₂⁵	C₂²×D₁₃	1	2	yes	—
322	C₂×#41	—	13	64	no	—
323	C₂×#41	—	26	192	no	—
324	C₂²×Q₈	—	13	12	no	—
325	C₂²×Q₈	—	26	8	no	—
326	C₂²×D₄	—	2	16	no	—
327	C₂²×D₄	—	2	192	no	—
328	C₂²×D₄	—	2	8	no	—
329	C₂²×D₄	—	13	12	no	—
330	C₂²×D₄	—	13	24	no	—
331	C₂²×D₄	—	13	24	no	—
332	C₂²×D₄	—	26	8	no	—
333	C₂²×D₄	—	26	16	no	—
334	C₂²×D₄	—	52	8	no	—
335	C₂²×D₄	C₂²⋊D₁₃	1	16	yes	complemented
336	C₂²×D₄	C₂²×D₁₃	1	24	yes	—
337	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
338	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
339	C₂²×D₄	C₂²×D₁₃	1	64	yes	complemented
340	C₂³×C₄	—	2	8	no	—
341	C₂³×C₄	—	13	24	no	—
342	C₂³×C₄	—	13	1	no	—
343	C₂³×C₄	—	13	1	no	—
344	C₂³×C₄	—	13	2	no	—
345	C₂³×C₄	—	13	1	no	—
346	C₂³×C₄	—	13	2	no	—
347	C₂³×C₄	—	13	24	no	—
348	C₂³×C₄	—	13	12	no	—
349	C₂³×C₄	—	26	16	no	—
350	C₂³×C₄	—	26	8	no	—
351	C₂³×C₄	—	52	8	no	—
352	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
353	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
354	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
355	#124	—	13	64	no	—
356	#123	—	13	128	no	—
357	C₂²⋊Q₈	—	13	64	no	—
358	#121	—	13	64	no	—
359	#121	—	13	128	no	—
360	#120	—	13	128	no	—
361	C₄×D₄	—	13	64	no	—
362	C₄×D₄	—	13	64	no	—
363	C₂×C₄⋊C₄	—	13	12	no	—
364	C₂×C₄⋊C₄	—	13	12	no	—
365	C₂×C₄⋊C₄	—	13	24	no	—
366	C₂×C₂²⋊C₄	—	13	12	no	—
367	C₂×C₂²⋊C₄	—	13	24	no	—
368	C₂×C₂²⋊C₄	—	13	24	no	—
369	C₂×C₂²⋊C₄	—	13	24	no	—
370	C₂×C₂²⋊C₄	—	13	128	no	—
371	C₂×C₂²⋊C₄	—	13	24	no	—
372	C₂×C₂²⋊C₄	—	13	24	no	—
373	C₂×C₂²⋊C₄	—	13	12	no	—
374	C₂×C₄²	—	13	12	no	—
375	C₂×C₁₃	—	2	8	no	—
376	C₂×C₁₃	—	2	16	no	—
377	C₂×C₁₃	—	4	8	no	—
378	C₂×C₁₃	C₂×#546	1	12	yes	complemented
379	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
380	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
381	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
382	D₁₃	—	4	4	no	—
383	C₂⁴	—	2	8	no	—
384	C₂⁴	—	2	8	no	—
385	C₂⁴	—	2	4	no	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	2	8	no	—
388	C₂⁴	—	2	96	no	—
389	C₂⁴	—	2	8	no	—
390	C₂⁴	—	2	96	no	—
391	C₂⁴	—	2	8	no	—
392	C₂⁴	—	4	48	no	—
393	C₂⁴	—	4	128	no	—
394	C₂⁴	—	13	6	no	—
395	C₂⁴	—	26	4	no	—
396	C₂⁴	—	26	4	no	—
397	C₂⁴	—	26	4	no	—
398	C₂⁴	#6129	1	8	yes	complemented
399	C₂⁴	C₂×C₂²⋊D₁₃	1	16	yes	—
400	C₂⁴	C₂³×D₁₃	1	12	yes	—
401	C₂⁴	C₂³×D₁₃	1	32	yes	—
402	C₂⁴	C₂³×D₁₃	1	6	yes	—
403	C₂⁴	C₂³×D₁₃	1	12	yes	—
404	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
405	#41	—	26	256	no	—
406	C₂×Q₈	—	13	16	no	—
407	C₂×Q₈	—	26	48	no	—
408	C₂×D₄	—	2	96	no	—
409	C₂×D₄	—	2	256	no	—
410	C₂×D₄	—	2	48	no	—
411	C₂×D₄	—	13	16	no	—
412	C₂×D₄	—	13	32	no	—
413	C₂×D₄	—	13	32	no	—
414	C₂×D₄	—	26	48	no	—
415	C₂×D₄	—	26	96	no	—
416	C₂×D₄	—	52	48	no	—
417	C₂×D₄	C₂×C₂²⋊D₁₃	1	96	yes	complemented
418	C₂×D₄	C₂³×D₁₃	1	32	yes	—
419	C₂×D₄	C₂³×D₁₃	1	16	yes	—
420	C₂×D₄	C₂³×D₁₃	1	16	yes	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	48	no	—
423	C₂²×C₄	—	13	6	no	—
424	C₂²×C₄	—	13	6	no	—
425	C₂²×C₄	—	13	12	no	—
426	C₂²×C₄	—	13	6	no	—
427	C₂²×C₄	—	13	12	no	—
428	C₂²×C₄	—	13	32	no	—
429	C₂²×C₄	—	13	32	no	—
430	C₂²×C₄	—	13	16	no	—
431	C₂²×C₄	—	26	4	no	—
432	C₂²×C₄	—	26	4	no	—
433	C₂²×C₄	—	26	8	no	—
434	C₂²×C₄	—	26	4	no	—
435	C₂²×C₄	—	26	8	no	—
436	C₂²×C₄	—	26	96	no	—
437	C₂²×C₄	—	26	48	no	—
438	C₂²×C₄	—	52	48	no	—
439	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	—
440	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
441	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
442	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
443	C₄⋊C₄	—	13	16	no	—
444	C₄⋊C₄	—	13	16	no	—
445	C₄⋊C₄	—	13	32	no	—
446	C₂²⋊C₄	—	13	16	no	—
447	C₂²⋊C₄	—	13	32	no	—
448	C₂²⋊C₄	—	13	32	no	—
449	C₂²⋊C₄	—	13	32	no	—
450	C₂²⋊C₄	—	13	32	no	—
451	C₂²⋊C₄	—	13	32	no	—
452	C₂²⋊C₄	—	13	16	no	—
453	C₄²	—	13	16	no	—
454	C₁₃	C₂²×#546	1	1	yes	characteristic, complemented, Sylow
455	C₂³	—	2	32	no	—
456	C₂³	—	2	64	no	—
457	C₂³	—	2	24	no	—
458	C₂³	—	2	24	no	—
459	C₂³	—	2	12	no	—
460	C₂³	—	2	12	no	—
461	C₂³	—	2	24	no	—
462	C₂³	—	2	64	no	—
463	C₂³	—	2	24	no	—
464	C₂³	—	2	64	no	—
465	C₂³	—	2	24	no	—
466	C₂³	—	4	32	no	—
467	C₂³	—	4	384	no	—
468	C₂³	—	4	32	no	—
469	C₂³	—	13	4	no	—
470	C₂³	—	26	12	no	—
471	C₂³	—	26	12	no	—
472	C₂³	—	26	12	no	—
473	C₂³	—	52	16	no	—
474	C₂³	C₂×#6129	1	4	yes	—
475	C₂³	C₂×#6129	1	24	yes	complemented
476	C₂³	#88251	1	4	yes	—
477	C₂³	C₂²×C₂²⋊D₁₃	1	48	yes	—
478	C₂³	C₂²×C₂²⋊D₁₃	1	4	yes	—
479	C₂³	C₂⁴×D₁₃	1	8	yes	—
480	C₂³	C₂⁴×D₁₃	1	4	yes	—
481	C₂³	C₂⁴×D₁₃	1	8	yes	—
482	C₂³	C₂⁴×D₁₃	1	3	yes	—
483	Q₈	—	26	32	no	—
484	D₄	—	2	64	no	—
485	D₄	—	2	32	no	—
486	D₄	—	26	32	no	—
487	D₄	—	26	64	no	—
488	D₄	—	52	32	no	—
489	D₄	C₂²×C₂²⋊D₁₃	1	64	yes	complemented
490	C₂×C₄	—	2	12	no	—
491	C₂×C₄	—	2	32	no	—
492	C₂×C₄	—	13	4	no	—
493	C₂×C₄	—	13	4	no	—
494	C₂×C₄	—	13	8	no	—
495	C₂×C₄	—	13	4	no	—
496	C₂×C₄	—	13	8	no	—
497	C₂×C₄	—	26	12	no	—
498	C₂×C₄	—	26	12	no	—
499	C₂×C₄	—	26	24	no	—
500	C₂×C₄	—	26	12	no	—
501	C₂×C₄	—	26	24	no	—
502	C₂×C₄	—	26	64	no	—
503	C₂×C₄	—	26	32	no	—
504	C₂×C₄	—	52	32	no	—
505	C₂×C₄	C₂²×C₂²⋊D₁₃	1	24	yes	—
506	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
507	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
508	C₂²	—	2	48	no	—
509	C₂²	—	2	96	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	8	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	8	no	—
515	C₂²	—	2	8	no	—
516	C₂²	—	2	8	no	—
517	C₂²	—	4	128	no	—
518	C₂²	—	4	48	no	—
519	C₂²	—	26	4	no	—
520	C₂²	—	26	4	no	—
521	C₂²	—	26	4	no	—
522	C₂²	—	52	24	no	—
523	C₂²	#11719511	1	16	yes	direct product factor
524	C₂²	C₂²×#6129	1	6	yes	—
525	C₂²	C₂²×#6129	1	8	yes	complemented
526	C₂²	C₂×#88251	1	6	yes	—
527	C₂²	C₂³×C₂²⋊D₁₃	1	16	yes	—
528	C₂²	C₂³×C₂²⋊D₁₃	1	6	yes	—
529	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	26	4	no	—
532	C₄	—	26	8	no	—
533	C₄	—	26	4	no	—
534	C₄	—	26	4	no	—
535	C₄	—	26	8	no	—
536	C₄	C₂³×C₂²⋊D₁₃	1	8	yes	—
537	C₂	—	2	8	no	—
538	C₂	—	2	16	no	—
539	C₂	—	4	8	no	—
540	C₂	—	52	4	no	—
541	C₂	C₂×#11719511	1	12	yes	direct product factor
542	C₂	C₂⁴×C₂²⋊D₁₃	1	1	yes	characteristic
543	C₂	C₂³×#6129	1	1	yes	characteristic
544	C₂	C₂²×#88251	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂⁴×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂⁴×D₄	D₁₃
hypocenter	C₁₃	C₂²×#546
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×D₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂³×#6129	C₂	semidirect
2. C₂×#11719511	C₂	direct (N × H)
3. C₂²×#88190	C₂	semidirect
4. C₂²×#88189	C₂	semidirect
5. C₂²×#88178	C₂	semidirect
6. C₂²×#88193	C₂	semidirect
7. C₂²×#88192	C₂	semidirect
8. C₂²×#88207	C₂	semidirect
9. C₂²×D₄×Dic₁₃	C₂	semidirect
10. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
11. C₂³×C₂²⋊Dic₁₃	C₂	semidirect
12. C₂⁴×D₄×C₁₃	C₂	semidirect
18. C₂³×D₄×C₁₃	C₂²	semidirect
21. C₂³×C₂²⋊D₁₃	C₂²	semidirect
22. C₂³×C₂²⋊D₁₃	C₂²	semidirect
23. C₂⁴×Dic₁₃	C₂²	semidirect
24. C₂⁴×Dic₁₃	C₂²	semidirect
26. C₂²×#6129	C₂²	semidirect
27. C₂³×C₄×D₁₃	C₂²	semidirect
28. C₂³×Dic₂₆	C₂²	semidirect
29. C₂×#88207	C₂²	semidirect
32. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
33. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
34. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
35. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
36. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
37. #11719511	C₂²	direct (N × H)
38. C₂×#88193	C₂²	semidirect
39. C₂×#88192	C₂²	semidirect
40. C₂×#88190	C₂²	semidirect
41. C₂×#88189	C₂²	semidirect
42. C₂×D₄×Dic₁₃	C₂²	semidirect
43. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
44. C₂²×#6103	C₂²	semidirect
45. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
46. C₂×#88178	C₂²	semidirect
47. C₂²×#6101	C₂²	semidirect
48. C₂²×#6101	C₂²	semidirect
49. C₂²×C₄×Dic₁₃	C₂²	semidirect
61. C₂²×D₄×C₁₃	D₄	semidirect
65. C₂²×D₄×C₁₃	C₂³	semidirect
74. C₂²×C₂²⋊D₁₃	C₂³	semidirect
75. C₂²×C₂²⋊D₁₃	C₂³	semidirect
83. C₂³×Dic₁₃	C₂³	semidirect
84. C₂³×Dic₁₃	C₂³	semidirect
86. C₂×#6129	C₂³	semidirect
88. C₂²×C₄×D₁₃	C₂³	semidirect
90. C₂²×Dic₂₆	C₂³	semidirect
91. #88207	C₂³	semidirect
94. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
95. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
96. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
97. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
98. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
99. #88193	C₂³	semidirect
100. #88192	C₂³	semidirect
101. #88190	C₂³	semidirect
102. #88189	C₂³	semidirect
103. D₄×Dic₁₃	C₂³	semidirect
104. C₄×C₂²⋊D₁₃	C₂³	semidirect
105. C₂×#6103	C₂³	semidirect
106. C₂×C₄⋊Dic₁₃	C₂³	semidirect
107. #88178	C₂³	semidirect
108. C₂×#6101	C₂³	semidirect
109. C₂×#6101	C₂³	semidirect
110. C₂×C₄×Dic₁₃	C₂³	semidirect
124. C₂⁴×C₁₃	#41	semidirect
137. C₂×D₄×C₁₃	C₂×D₄	semidirect
151. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
152. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
165. C₂²×Dic₁₃	C₂⁴	semidirect
166. C₂²×Dic₁₃	C₂⁴	semidirect
169. C₂×C₄×D₁₃	C₂⁴	semidirect
171. C₂×Dic₂₆	C₂⁴	semidirect
174. C₂²⋊Dic₁₃	C₂⁴	semidirect
175. C₂²⋊Dic₁₃	C₂⁴	semidirect
176. C₂²⋊Dic₁₃	C₂⁴	semidirect
177. C₂²⋊Dic₁₃	C₂⁴	semidirect
178. #6103	C₂⁴	semidirect
179. C₄⋊Dic₁₃	C₂⁴	semidirect
180. #6101	C₂⁴	semidirect
181. #6101	C₂⁴	semidirect
182. C₄×Dic₁₃	C₂⁴	semidirect
184. C₂⁴×D₄	D₁₃	semidirect
212. C₂³×C₁₃	C₂×#41	semidirect
225. D₄×C₁₃	C₂²×D₄	semidirect
259. C₂³×D₄	C₂×D₁₃	semidirect
296. C₂²×C₁₃	#546	semidirect
300. C₂²×C₁₃	C₂²×#41	semidirect
335. C₂²×D₄	C₂²⋊D₁₃	semidirect
339. C₂²×D₄	C₂²×D₁₃	semidirect
378. C₂×C₁₃	C₂×#546	semidirect
398. C₂⁴	#6129	semidirect
417. C₂×D₄	C₂×C₂²⋊D₁₃	semidirect
454. C₁₃	C₂²×#546	semidirect
475. C₂³	C₂×#6129	semidirect
489. D₄	C₂²×C₂²⋊D₁₃	semidirect
523. C₂²	#11719511	direct (N × H)
525. C₂²	C₂²×#6129	semidirect
541. C₂	C₂×#11719511	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×#6129	2
C₂×#11719511	2
C₂²×#88190	2
C₂²×#88189	2
C₂²×#88178	2
C₂²×#88193	2
C₂²×#88192	2
C₂²×#88207	2
C₂²×D₄×Dic₁₃	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂³×C₂²⋊Dic₁₃	2
C₂⁴×D₄×C₁₃	2
C₂²×#546	13

Subgroups — C22×#11719511 #16769839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719511 #16769839